What is the total volume of a greenhouse that is 150 feet long, 20 feet wide, 10 feet high at the sides, and 15 feet high in the center?

To determine the total volume of the greenhouse, it is helpful to visualize its structure. The greenhouse can be approximated as a rectangular base topped by a trapezoidal roof.

First, calculate the volume of the rectangular part of the greenhouse:

• The length is 150 feet, the width is 20 feet, and the height at the sides is 10 feet.

• The volume of the rectangular base is determined by multiplying these dimensions together:

Length × Width × Height = 150 ft × 20 ft × 10 ft = 30,000 cubic feet.

Next, address the volume of the trapezoidal section above the rectangular base. This part has a different height, as it reaches a maximum of 15 feet in the center.

The height of the trapezoidal section can be found by subtracting the height of the sides from the maximum height:

• Maximum height at center - height of the sides = 15 ft - 10 ft = 5 ft.

The trapezoidal roof can be viewed as a prism where the area of its base is a rectangle that measures the same width (20 feet) and has an average height of the trapezoidal section:

• The average height of the trapezoidal